Question 180: Laws of Motion

Question

A light string passing over a smooth light pulley connects two blocks of masses ${m_1}$ and ${m_2}$ (vertically). If the acceleration of the system is $g/8$, then the ratio of the masses is

Accepted Answer

Assume that, mass m
1
is greater than mass m
2
, so the heavier mass m
1
is accelerating downward and the lighter mass m
2
is accelerating upwards.
For mass ${m_1}$ the equation will be
${m_1}$$g-T=$${m_1}$$a$
For mass ${m_2}$ the equation will be
$T-$${m_2}$$g=$${m_2}$$a$
Adding those equations we get
$a = {{\left( {{m_1} - {m_2}} ight)g} \over {{m_1} + {m_2}}}$
$	herefore$ ${g \over 8} = {{\left( {{m_1} - {m_2}} ight)g} \over {{m_1} + {m_2}}}$
$ \Rightarrow {1 \over 8} = {{{{{m_1}} \over {{m_2}}} - 1} \over {{{{m_1}} \over {{m_2}}} + 1}}$
$ \Rightarrow$ ${{{m_1}} \over {{m_2}}} + 1 =$ ${8\left( {{{{m_1}} \over {{m_2}}} - 1} ight)}$
$ \Rightarrow$ ${{{m_1}} \over {{m_2}}} = {9 \over 7}$

Answer

$8:1$

Answer

$9:7$

Answer

$4:3$

Answer

$5:3$

Laws of Motion

A light string passing over a smooth light pulley connects two blocks of masses {m_1} and {m_2} (vertically). If the acceleration of the system is g/8, then the ratio of the masses is

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